论文标题

Maxwellian棘轮的功能热力学:构建和解构模式,随机和降低行为

Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors

论文作者

Jurgens, Alexandra M., Crutchfield, James P.

论文摘要

Maxwellian棘轮是实现输入输出信息转换的自主,有限状态的热力学引擎。对这些“恶魔”的先前研究重点是它们如何利用环境资源来产生工作:它们随机分配了有序的投入,利用增加的香农熵将能源从热储层转移到工作库中,同时尊重liouvillian国家空间空间动力学和第二种法律。但是,迄今为止,正确确定此类功能热力学操作机制仅限于很少的引擎,该引擎可以准确且以封闭形式计算其信息自由度之间的相关性 - 这是一个受到限制的集合。此外,棘轮行为的关键第二维度在很大程度上被忽略了 - 棘轮不仅会改变环​​境输入的随机性,其操作构造和解构模式。为了解决这两个维度,我们调整了动态系统和奇异理论的最新结果,这些结果有效,准确地计算了一般隐藏的马尔可夫过程的熵率和统计复杂性差异的速率。这些方法与信息处理第二定律协同确定了有限国家的麦克斯韦恶魔的热力学工作制度,该恶魔具有任意数量的状态和过渡。此外,它们促进了分析结构与给定引擎做出的随机性权衡。结果是对信息引擎的信息处理功能的观点大大增强。作为应用程序,我们对Mandal-Jarzynski Ratchet进行了彻底的分析,表明它具有无限的有效状态空间。

Maxwellian ratchets are autonomous, finite-state thermodynamic engines that implement input-output informational transformations. Previous studies of these "demons" focused on how they exploit environmental resources to generate work: They randomize ordered inputs, leveraging increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir while respecting both Liouvillian state-space dynamics and the Second Law. However, to date, correctly determining such functional thermodynamic operating regimes was restricted to a very few engines for which correlations among their information-bearing degrees of freedom could be calculated exactly and in closed form---a highly restricted set. Additionally, a key second dimension of ratchet behavior was largely ignored---ratchets do not merely change the randomness of environmental inputs, their operation constructs and deconstructs patterns. To address both dimensions, we adapt recent results from dynamical-systems and ergodic theories that efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov processes. In concert with the Information Processing Second Law, these methods accurately determine thermodynamic operating regimes for finite-state Maxwellian demons with arbitrary numbers of states and transitions. In addition, they facilitate analyzing structure versus randomness trade-offs that a given engine makes. The result is a greatly enhanced perspective on the information processing capabilities of information engines. As an application, we give a thorough-going analysis of the Mandal-Jarzynski ratchet, demonstrating that it has an uncountably-infinite effective state space.

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